For the NS-NS sector, generating functional
of string products with the \(L_\infty \)  structure, \(L^{NS\textrm {-}NS}(s,\bar{s},t)\)  , has been
constructed by imposing the differential equations [1]},
\(&\ \partial _tL^{NS\textrm {-}NS}(s,\bar{s},t)\ =\ [L^{NS\textrm {-}NS}(s,\bar{s},t)\,, (\lambda ^{NS\textrm {-}NS}+\bar{\lambda }^{NS\textrm {-}NS})(s,\bar{s},t)]\,,\\&\ \partial _sL^{NS\textrm {-}NS}(s,\bar{s},t)\ =\ [\eta \,, \lambda ^{NS\textrm {-}NS}(s,\bar{s},t)]\,,\qquad [\eta \,,\bar{\lambda }^{NS\textrm {-}NS}(s,\bar{s},t)]\ =\ 0\,,\\&\ \partial _{\bar{s}}L^{NS\textrm {-}NS}(s,\bar{s},t)\ =\ [\bar{\eta }\,, \bar{\lambda }^{NS\textrm {-}NS}(s,\bar{s},t)]\,,\qquad [\bar{\eta }\,,\lambda ^{NS\textrm {-}NS}(s,\bar{s},t)]\ =\ 0\,,\) 
